A resonator is a key component in various timing and frequency reference applications. Resonators are actuated to oscillate close to their natural, characteristic resonant frequency that is determined by the material, shape and/or characterizing dimensions of the resonator or the like-component serving such a function.
For use in reference and timing functions, accurate controllability/settability of the operating frequency is a must. In typical applications, the inaccuracy of frequency control may be allowed to be in the range of 1-100 ppm (parts per million). Such a ppm-level precision sets tight limits for the manufacturing tolerances. Moreover, additional mechanical and/or electrical fine-tuning is often necessary in the final adjustment.
Micromechanical resonators are widely used in MEMS-based equipment as their key component. As examples of such pieces of equipment may be mentioned microgyro-scopes, microvibromotors, micromachines and microwave systems. The resonators are driven by electrostatic actuation so as to oscillate close to their characteristic, natural resonant frequency.
Additionally, micromechanical resonators can be used to complement embodiments of quartz-resonator-based technology in frequency-reference devices, whereby their frequency accuracy must be improved before they can entirely replace quartz-based oscillator technology in certain applications.
Micromechanical resonators are fabricated by combining optical lithography and etching techniques in a fashion required in this category of scale so as to offer benefits over conventional quartz-based resonator technology. However, the manufacturing process can cause variations up to several percent in the dimensions of the devices being manufactured.
For better understanding of prior-art solutions vs. the embodiments of the present invention, reference is next made to FIGS. 1A ja 1B as follows:                FIG. 1A shows the basic structure of a prior-art resonator.        FIG. 1B shows a lumped mechanical model of a prior-art resonator.        
Accordingly, FIG. 1A illustrates the basic structure of a prior-art resonator as such. A simple resonator comprises a spring element (beam) and a rectangular mass element (mass). The spring element can be, e.g., a mechanical cantilever spring (beam) as illustrated in FIG. 1.
In a simple resonator of FIG. 1A, the characteristic resonant frequency ω0 is
                                          ω            0                    =                                    k              m                                      ,                            (        1        )            where the spring constant k is
                    k        =                  Y          ⁢                                          ⁢                                                                      w                  3                                ⁢                h                                            4                ⁢                                  L                  3                                                      .                                              (        2        )            
FIG. 1B illustrates a lumped model of a prior-art basic resonator. Herein, Y is the Young's modulus for the spring material, w is the width of the spring element, h is the height thereof and L is the characteristic length thereof. The width w of the spring element is typically quite small and, due to cubic-law dependence, the resonant frequency ω0 is sensitive to variations in the spring element width w.
First-order change in the resonant frequency ω0 in relation to change in the spring element width is
                                                        Δω              0                                      ω              0                                =                                    3              2                        ⁢                                          Δ                ⁢                                                                  ⁢                w                            w                                      ,                            (        3        )            where ∂ω0 is infinitesimal change of frequency caused by an infinitesimal change ∂ω in the spring element width. One of the most significant problems in the design of micro-mechanical resonators is the variation of the resonant frequency, which is caused by insufficiently controlled or otherwise poor precision in the mechanical dimensions of the resonator structures.
For instance, assessed on the basis of Eq. 3, it can be seen that if the spring element width varies by 4%, also the resonant frequency varies, however, as much as 6% or 60,000 ppm.
Related hereto, patent publication WO 2009/092846 A1 describes a prior-art method for controlling the effects of manufacturing precision on problems concerning frequency variations.
It must be understood, however, that under disturbance situations the forces imposed on a resonator affect its function through subjecting the resonator and/or parts thereof to acceleration. Hereby, the resonator structures are deformed and its oscillating movements may be interfered even if the resonator would have a robust design. The effects of strong disturbing forces may additionally cause wide-amplitude movements of long spring-like structures supported by one end only, whereby they may under certain conditions hit other parts of the structure and even undergo mechanical damage or interfere with the electrical signals used for controlling the operation of the structure. To cope with such instances, it is necessary to design the interelectrode gaps with a guard distance that in capacitive resonators, for instance, may cause problems when a sufficiently high capacitance must attained in a relatively small structure. On the other hand, the goal toward a higher capacitance may require adding more mass to the spring elements which resultingly may affect the resonance frequency in an undesirable manner through the inertia of the mass, for instance.